The noisy sensor Consider the situation in Figure 14.4. Sensor nodes are laid out on a square grid of spacing

d. Propagation losses go as the second power of distance. The source to be detected is Gaussian with zero mean and variance 2s

, and the noise added at each sensor is independent AWGN with variance 2 n. Sensor node 1 is malfunctioning, producing noise variance 102 n. The two best nodes in terms of SNR will cooperate to provide estimates of the source.

(a) Sketch the region of the source locations over which node 1 is among the two best nodes, assuming a long sequence of measurements are made of the source.

(b) For a single measurement, approximate the likelihood that a source at position

(0.25d, 0) will result in better SNR at sensor 5 than at sensor 1.

Transcribed Image Text:

6 2 1 3 5 Figure 14.4 The sensor array. 4